Transforming Blender Render Textures to Cycles Textures
I'm not sure what you mean by eliminating noise in Blender Render if you are moving to cycles, but if you are looking to remove noise in cycles, there is already several answers in Blender StackExchange FAQ: Frequently Asked Questions on Blender Stack Exchange

BlenderGuru made also a great article about the topic: https://www.blenderguru.com/articles/7-ways-get-rid-fireflies/

For the second question, by looking at your texture I assume you want pixelated look. Answer is very simple, you can turn back your mips and get rid of the filter. All you need to do is set Sampling, the second field under the image name field currently have set as Linear to Closest.